Branson, who campaigned for a Remain vote, said many voters had been misled by the Leave campaign which won on Friday morning, and should sign the controversial petition, which demands a new vote.
Writing on his blog, he accused leave campaigners of backtracking on key pledges on immigration and NHS funding, said $2 trillion (£1.5 trillion) had been wiped off the world's share prices since the Brexit vote, while UK markets lost more money in one day than the country had paid in since it joined.
“The decision over the UK's future was based on false promises that pushed a minority of the UK's total voting population (17 million out of 46 million) to vote the way it did. Two years before Brexit will even become reality, according to EU rules, it is already having massive consequences on the UK economy, and on society. Brexit has fractured the country more than any other event in recent memory,” Branson said.
“The vast majority of MPs voted in by the electorate want the UK to stay part of Europe. In light of the misrepresentations of the Leave campaign, Parliament should reject the results of this non-binding referendum as Nicola Sturgeon has announced she will do in Scotland’s Parliament.”
The petition, which has been signed by 3.6m people, was originally set up before last week's vote and called on the government to hold a second referendum if either side won by less than 60 per cent, based on a turnout of less than 75 per cent.
It has seen a surge of signatures from the Remain camp since Friday's verdict, although large numbers of supporters have since been removed following an investigation.
|Brexit Britain: What you need to know|